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The Great Pyramid of Jizeh 



1 he vjrreat r yramid 



Of JiZEH 



THE (?LAjN AjNO 0(BJECT 



?)S 



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Of its Construction 



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CINCINNATI 
ROBERT CLARKE & CO 

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Entered according to Act of Congress, 
In the year one thousand eight hundred and seventy-one, 

By ROBERT CLARKE & CO. 
In the Office of the Librarian of Congress, at Washington. 




The Great Pyramid of Jizeh. 



THE PLAN AND OBJECT OF ITS CONSTRUCTION. 

assertion as to a discovered solution of 
the plan and object of this huge mass, so 
venerable, so covered with the mists of pri- 
^ meval time, must be made u'ith very much of 
reserve. If it has, in its stony strength, been through 
the long centuries replete vi'ith instruction, easily to be 
read and understood by one understanding the significancy 
of its symbolization, he vi^ho at last solves the riddle of its 
language must, in self-defense, attribute the cause of solu- 
tion to anything but himself, or any faculty which he may 
possess. It is, perhaps, the better part to consider the abil- 
ity as a temporaty gift for a special purpose. The doing 
so has at least a merit in the possession of one well-recog- 
nized truth, viz.. That many more important discoveries 
are made by persons of very little pretension to learning. 

All that the author has in the way of information about 
this pyramid is contained (i) in an article in the Jtneri- 
can Quarterly Church Review for April, 1869, and (2) in 
the work of Professor C. Piazzi Smyth, called Our Inher- 
itance in the Great Pyramid of 'Ji%eh. 

It seems it has been thought, by many, that the pyramid 
was built to perpetuate a standard of measure, or, rather, 
standards of measure. The thought was suggested by M, 
Jomard, of the French expedition ; afterward by the Rev. 
Mr. Taylor, of England, and later by Professor Smyth. 



Great Pyramid cf Jizeh. 



What the full extent of Mr. Taylor's researches led him to 
conclude in all, is not known j one fact stated by him, 
however, fastened itself upon the attention, viz.. That the 
hight was to the side of base multiplied by two, as i : 
3. 144, or rudely, as an approximation of the diameter to the 
circumference of a circle. The work of Professor Smyth 
is full of the most valuable information as to accurate ad- 
measurements of different portions of the pyramid, without 
and within j as to linear measures, and those of angles. 
That in his work, which again riveted the attention, was 
that, upon the ascertainment of the best possible admeas- 
urements, Hight : Side of base X 2 : : i : 3.14159+ ; 
the accordance of ratio to that of diameter to circumfer- 
ence being exact to the fifth decimal place, but failing 
beyond that. 

Considerable thought led to some conclusions which 
were taken as guides in investigation. Professor Smyth 
was convinced that the mass held treasures of knowledge 
— not of a lost civilization, but laid up under the dictation 
of a divine power. For, if such treasures did exist (such 
seems the running of his thought), it was less marvelous 
to judge that they were thus given, than that they be- 
longed to that of which every possible vestige but this one 
had vanished off the face of the earth. 

Taking it that it was a work divinely inspired, it seemed 
(i) that its construction would be characterized by the 
greatest simplicity, for God's work is very simple ; (2) 
that God would never perpetuate a standard of measure in 
numbers arbitrarily chosen, because by detriment to the 
pyramid the numbers might be impaired, and the correct- 
ness of the standard lost. Therefore, in simplicity, the 
value of the work should lay in the very elemental princi- 



Its Plan and Object. 



pies of its construction, so that if one could but find the 
key of its construction, any unit of measure taken in num- 
bers would bring out the proper results. 

First, therefore, as to simplicity. If the pyramid was 
intended to represent earth admeasurements, there would 
be that about its shape suggestive, in a simple way, of the 
object of its design. That which would seem to be the 
most suggestive would be a pyramid, the square of whose 
base would represent the inscribed upon the great equatorial 
circle, and whose hight would indicate the pole (one-half the 
polar diameter). Since it is not so, and is irregular in this 
connection, it departs- from simplicity of design. Still, this 
should be for as simple an object. What was the object ? 
It was noticed that Professor Smyth makes the Hight : Side 
of base X 2 : : i : 3. 14159+, by the best of the actual 
measures, agreeing with the relation of diameter to circum- 
ference to the fifth decimal place, and there departing. 
This, he says, is a very close approximation. Here, it 
seemed, was the first step to the key. The reason of the 
departure from a simple design of the earth's shape was 
because the pyramid was, first, a standard of measure of 
the relation of diameter to circumference, in terms of right 
lines and shapes. If this were so, and the work divine, 
God never had to approximate to anything, nor did He 
ever labor under the necessity of raising a system of ap- 
proximates upon the falsehood of the equality of ultimate 
ratios as given in the Principia. He has, and would give, 
the exactitude. So let it be taken tiiat the pyramid's first 
construction was the relation of diameter to circumfer- 
ence. But where the numbers to apply ? Mr. John A. 
Parker gives them in his neglected work upon the quadra- 
ture, viz., 6561 : 20612 in integrals, jljr^f^^ hy the severest 



Great Pyramid of Jizeh. 



tests. This step gained, does the pyramid apply to earth 
admeasurements ? 

ACC represents the meridianal section. 

CC length of 

one side of base. 

ADD' repre- 
sents the trans- 
verse section. 

DD' being di- 
agonal of base. 

Hight AB == 
6561. 

One-half side 
of base CB = 

5153- 




t/BC2X2=BD=7287.442486+. 



-E- 



K 



By thus placing the ele- 
ments of construction in ver- 
tical section, we have com- 
bined in one showing all the 
elements of measure of the 
pyramid. 



Now, it seemed, perhaps, that using the pyramidal rela- 
tion of diameter to circumference, it might in some way 
be made in nature to apply to the earth ; and there was 
one way to try it, viz., to put it in the earth or in the top 
of a great circle, and see how it fitted in its relations. If 



Its Plan and Object. 7 

the earth were a great circle, by putting ADD' in a circle, 
so that the circumference would cut in A and D and D', 
the application of measurement might be made. It is tried 
in the diagram. The interior lines at E and F are, as well 
as all the others, out of drawing, because, if correct, they 
could not show to the eye the difference which comes out. 
DB exceeds AB. Therefore to construct a circle cutting: 
both points, prolong AB till AB + BF=DB. Now if 
DB, in position, were at F, or dropped down that low, one 
could use AF as a radius, which would cut D. But 
because it is as it is, a radius AF from F as a center can 
not cut D. Therefore a further addition is necessary, and 
you extend the line AF until AE is just the length re- 
quired for a radius, which, with E as a center, will cut in 
D and D'. This radius is easily obtained, because DB is 
a mean proportional between AB and some length x, 

which gives = radius required. The new radi- 
us = AE=7327.6588i6-f 
AB=656i. 
DB=7287.442486+ 
First difference, DB — AB=;726.44248 
Second difference, AE — DB or AF=:40.2i633o 
(Mark, that if the decimal 21.6330 were taken and 
pointed as done, it would agree in miles with the differ- 
ence between equatorial and polar diameter, thus : 21.6330 

21.6318 

00.0012 
or within five feet. This is noteworthy because the pyra- 
mid seems to run on differences in measures applied.) 

Now we have to make comparisons with earth admeas- 



Great Pyramid of Jizeh. 



urements, bearing in mind always that we have been using 
a perfectly circular standard of measure, not an elliptical one. 
A little digression is here necessary, because of an ac- 
cidentally discovered relation which may be of value. 
The measure of the earth's diameters was wanted as a 
standard of reference, and having no first authority on the 
subject directly at hand, reference was made to a book on 
earth relations which had been presented by one young 
friend to another as a Christmas gift, Flguier's Earth and 
Sea. In looking it over, that which was desired was given 
in feet^ viz : 

Equatorial diameter, 41852865. 

Polar diameter, 41738710. 



Difference, 114154. 

It occurred that if this difference was divided into the 
longer, the result would be a number of parts for equa- 
torial diameter, of which polar diameter would necessarily 
contain one less. The division was made; 

41852865^1 14154=366.54750. 

It was remembered that Mr. John A. Parker, in 
obtaining, in an elemental way, the exact measure of 
planetary time, found, as his standard by which to obtain 
others, the time measure of the earth about the sun to be 
366.43555+. The wonderful approximation of the chosen 
earth period above to this standard seemed to prove a 
necessary rhythmical relationship. To test it, divide 
41852865 by 366.43555+, and the result will be equal 
to 114216.16 

From this take above difference, 114154. 



And the result is, 62.16 



Its Plan and Object. 



That is, that, bv the permitted use of but 62.16-100 feet 
in 42. 000. 000, we have, in earth equatorial extension, an 
exact counterpart or multiple of its time extension. In 
other words, earth shape runs in rhythm with time exten- 
sion, or, the spheroid of the earth's shape has a harmonic 
relation to the ellipse of the earth's orbit. 

Time of Earth, 3^^43555 

Exact multiple of Earth's diameter 366.43555 

41852865 : 366.43555 : : 41738648.84 : 365.43555 

Relation of equatorial diameter 366-43555 

to polar diameter 365-43555 



Difference, i. 

In miles, 21. 6318 

Now, on the pyramid, the first difference was 726.44248. 
Divide by 2=363.22124, which, taken as one part for 
time as above, we have taken the difference twice : whereas 
above, with the earth, it was taken but once. 

Again, \ of base diagonal, or DBi=z7287.442486-f-2 

=3643.721243-^10 
=364.3721243 

Again, new dia. AE=7327.6588r6-=-2 
=3663.829416-4-10 
=366.3829416 

Compare this 366.3829416 

With earth and time standard 

above, 366-43555 

Difference, .05261 



lo Great Pyramid of Jizeh. 

in diminution, or minus about lOOO feet in the earth, or 
I hour's time in the year. 

The divisions by 2 and by lo are characteristic of the 
pyramid. It is seen how the pyramid, by a strictly circu- 
lar measure, brings out the elements of time and earth 
measure, without any effort or forced construction, but by 
the simple application of an original standard of circular 
measure. Our difference of earth diameters was one. Our 
pyramid measure of difference was taken twice. Apply it 
as we have the earth's 

AE= 366.3829416 

DB= 364.3721243 



Difference, 2.0108 173 

The harmony is something to admire and wonder at. 
Again, difference between AE and 06=40.216330. 
The shorter diameter 7287.442486 : 40.216330 :: 
7905.047128 miles, the shorter diameter of the earth ; 
43.693. As this is taken twice, 

43.693^2=21.846 
Earth difference, 21.631^ 



Difference, 


.215 


Larger diameter 7327.658816 : 40.216330 : 


: 7926.67897 : 


43-503- 




Divide 43.503 by 2= 


21.751 


Earth difference, 


21.631 



Difference, .120 

or within 500 feet or 1000 feet of the exact difference of 
earth diameters ; or, as a standard of time, difference from 
standard .052, or i hour in i year. 



Its Plan and Object. ii 

A very minute difFerence is observable, requiring an 
intercalation or change, of some kind, to bring the meas- 
ures up to an exactness of conformity with earth meas- 
ures. The use has been made of a pure circular 
measure, and the resultant differences, as shown, have 
brought out the elliptical property of the earth, requiring a 
very slight correction to bring out the exactitude. If an 
ellipse is required to be drawn cutting in A and D and D', 
it can not be done by any foci located in the horizontal 
diameter O O'. The foci will have to be taken on a line 
parallel to D D', and a little nearer to the line D D' than 
is O O'. It is thought that the change of relations by 
this would perhaps bring out the exact correction required. 
It may be by some use between the whole number 40. 
and the 40.216330, which would equal 

21.6330 
Compare with difference of earth diameters, viz: 21.6318 



Difference, .0012 

or about 5 feet. One thing, however, seems certain, the 
exact measure of the ellipse of the earth was known, not 
by experiment, but by the known rhythm that time exten- 
sion and earth shape were convertible terms. 

As to further construction. By completing the circle, 
a pyramid laid off on the opposite side would give the cube 
I K L M in the center; the term cube is used because it 
would be such a solid in a globe. But only one-half of 
this belongs to our pyramid. A moment's thought will 
show that this cube would make a chamber one-half as 
wide as long, and one-half as high as long. Therefore, as 
our earth and time measures come in the differences taken 



12 



Great Pyramid of Jizeh. 



up in this cubic chamber, we would naturally desire to 
preserve this as an epitome of the earth's shape and its 
time. But a perfect cube is expressive of a circle alone, 
and we want to place our second difference so as to desig- 
nate an ellipse. Let us, therefore, to bring out this excess 
as an ellipse, add our second difference twice., once on the 
/ G side and once on the K H side ; because we have, in 
the squares /and K^ taken our first difference twice. We 
have then our cubic 
chamber, and 40.+ 
added to each end, 
which 40. is the dif- 
ference which will 
exhibit the elliptical 
character of the 
earth's shape and its 
time. 

Reduce the above elements as follows : 
Length, 1452.8849^ 145.28 

Width, 726.44 >-^-byiO= 72.64 

Difference,* 80.00 J 8.00^ 

And the dimensions of the chamber will be : 
Length, 36.3 
Width, 18.1 
Hight, 20.1 
Difference between width and hight, 2. 

If we compare these measures with the exactest meas- 
ures of the king's chamber, as given by Piazzi Smyth, we 
find those dimensions to be : 



40 


1453. 8849 














^ 

"=il 








726.44 + 


726. M^- 


t> 





4:0 



36.32 
:l8.l6 

2.00 



*To be added to width for hight. 



Its Plan and Object. 13 

Length, 34 feet 3 inches.* 
Width, 17 feet I inch. 
Hight, 19 feet I inch. 
Difference between width and hight, 2. 

Showing an exact similarity of method in arriving at the 
results. 

Now, this reduction can be used either as an earth or 
time measure, and is appropriate as the King's chamber. 
The coffer, an epitome of the chamber itself, in its reduced 
form would become convenient as a standard of capac- 
ity and linear measure, etc. The symmetry is this : that 
the center of the coffer or of the chamber is the cos- 
mic point of rest about which terrestrial and celestial shapes 
take form and movement in rhythm. As extremes meet, 
one may go from shape to shape, and from movement to 
movement, always in harmonic rhythm, to arrive at last 
at the seat of that wonderful intelligence that causes 
all, little and great, the material seen and the material un- 
seen, to work in musical accord and in mathematical 
fitness. 

It is to be noted that the admeasurements of the coffer 
seem to be out of rhythm with those of the chamber ; but 
it will be seen, also, on examination, that, with relation to 
the measure of the room in tuhich it is located^ it, itself, is 
irregularly placed. This irregularity of position with respect 
to the chamber, is the peculiarity^ which will lead to the 
discovery of the reasons for the coffer dimensions. 

But we have, perhaps, only stepped upon the threshold 
of the unfolding wisdoms within. Parallels of latitude be- 
come significant and full of meaning. Solar and lunar 

*Our decimals reduced to twelfths would be 4, 2, 2. 



14 Great Pyramid of Jizeh. 

divisions of time are pronounced from the speaking stone 
in pure, truthful, mathematical lines. Perhaps the royal 
red of the King's chamber is significant in color of the sun, 
and the white marble of the Queen's chamber of the 
cold rays of the moon. 

A icw suggestions may not be inappropriate. If a square 
be placed upon the meridianal section protracted to a loz- 
enge shape, the side of that square will = 5814.536352. 
This would seem to designate a horizontal section through 
the pyramid, the summit of a cubic chamber, with the exact- 
itude of circular measure to compare by. This section 
would be at a distance from the apex of the pyramid of 
3653.731824, thus bringing out for use another number 
significant of time. Take this distance : 

3653.731824 
J of 1^ below is bottom of K.'s Ch., about 969.089392 



4622.821216 
J of J below is bottom of Q.'s Ch., about 969.089392 



5591. 910608 
|- of J below is bottom of Pyramid, 969.089392 



6561.000000 
J of J below is bottom of Subterranean, 1453.634088 

If we take side of square 5814.536352 and divide it by 
8, we have each eighth equal to - 726.817044 

Our first difference was _ - - 726.442486 

Difference, - - - - -374558 



Its Plan and Object. 



15 



Again the wonderful reproduction of numbers is ob- 
servable, with the addition of the minute differences. It 
should be stated that the square 5814.536352 is equal to the 
area of half the lozenge, within another difference exceed- 
ingly small. The rectification of all these differences is no 
doubt to be found in the pyramid, because its construction 
is elemental and purely geometric. It is probably because 
the strictly true interpretation of its wonderful speech has 
not even yet been arrived at. This division of 8 is proba- 
bly that of which the peculiar divisions of the King's cham- 
ber is significant. " Eight floors it, eight roofs it, eight 
flags the ends, and sixteen " (taken double because the cubic 
difference is taken twice) " the sides." 

The diagram being a representation of the square last 
spoken of, the angle BAC= 
26° 28', nearly. The use of the 
lines in the square bringing out this 
angle of 26° 28', seems to deter- 
mine both the location of the King's 
chamber, and also the passage-ways 
in the mass. As soon as the loca- 
tion of the chamber and the passage- 
ways is determined, the structure of B 
the grand gallery and the space be- 
tween it and the King's chamber will be easily reproduced. 
It seems probable, by looking at the peculiar shapes of the 
ends of the grand gallery extensions, that they come from 
the intersection of parallel lines with another order of lines 
crossing at peculiar angles in the square for special reasons. 
It may be that it is caused by the divisions of an equilateral 
triangle placed in the square. 




1 6 Greal Pyramid of Jizeh. 

If an equilateral triangle whose side = the side of the 
square be placed in the square, its vertex toward A, then 
if the triangle be divided as to its sides into eight equal 
parts, and the points of division be joined and protracted 
to sides of square, it will be found that the vertical 
angles will equal 60°, while some on the sides will equal 
120°. In the pyramid the King's chamber proper is capped 
by several other chambers, all terminating in a roof, the 
angle of which is judged to be 120°. It is noticeable that 
the excess for ellipticity appears in highi. This excess, 
however, is originally taken in horizontal extension along 
the equatorial diameter. Its position is, therefore, at right 
angles to that one in which the excess originates. It may 
be that the peculiar a7igle of the roof serves to indicate 
whence the hight was taken, and may serve, possibly, to 
explain the meaning of the other chambers, or the hight 
taken between the top of the King's chamber and the 
roof. 

These, however, are mere suggestions of thought not 
yet tested. But, truly and verily, the Ancient of days puts 
the achievements of modern science to the blush. The 
days of truth revived seem to be coming upon the inhabi- 
tants of the earth — happier and better days. Perhaps it 
may not be long before the light of new and exact knowl- 
edge will be shed abroad in the place of approximations, 
both in science and theology. 

There is, about the revelations made by the great pyra- 
mids that which is almost startling in its effect upon the 
imagination. When one considers that buried in the 
pyramid is the sacred cubit of the Hebrews ; that four 
times the English quarter is the capacity of the coffer ; that 
the English inch and English foot measure runs in such ad- 



Its Plan and Object. ly 

mirable rhythm with time and pyramid measures, it is not by 
any means extravagant to judge that a link of connection 
is found between the Anglo-Saxon and the Hebrew race. 
The thought once entertained finds no obstacle of an insu- 
perable kind in the way of its acceptation. The captivity 
of the ten tribes was located almost in the direct pathway 
of the emigration from the East into Europe and the north 
of Europe. It was placed in the tide ever impelling on to 
the north. Strong and particular emphasis is laid upon the 
north quarter as that from whence the lost shall be gathered 
to their brethren. 

"Go out and proclaim these words toward the north, and say. 
Return, thou back-sliding Israel." 

" In those days the house of Judah shall walk with the house of 
Israel, and they shall come together out of the land of the north 
to the land that I have given for an inheritance unto your fathers." 

" Behold I will bring them from the north country." 

" Which led the seed of the house of Israel out of the north 
country." 

" I will bring the blind by a way that they know not ; I will 
lead them in paths that they have not known." 

" Ho, ho, come forth, and flee from the land of the north." 

" Israel and Judah shall be brought together and made one 
nation." 

Were the blind eyes opened, it is quite possible that here 
in this New World of ours, one would suddenly come to 
the realization that he was dwelling in the midst of the 
teeming multitudes of Israel ; terminating their emigration 
in a land long promised, long reserved ; under government 
of a commonwealth restored ; free from every taint of caste 
condition, or of kingly rule. 



Appendix. 

1. In construction (page 7) it would be proper, if the 
number 40 was needed, to make three differences ; of 
which 2d might be 40 and the 3d .216330. 

2. The exact side of square (page 14) is thought to be 
5772.3806, This — 5814.536352=40. which may be 
of value in construction. 

3. If circumference (page 6) was that of an ellipse, a 
perpendicular dropped from 45° might touch C ; if so, 
the relation would be of importance. If as it is it lacks 
40. it may be that this want or difference is expressed in 
construction. 

4. If base of pyramid was made to rest upon the parallel 
of 45°, the hight thrown inward in the circle, it might 
show the reason of the elevation in the pyramid of the 
King's chamber. 

5. If one side of the square (page 15) was diminished 
by 40 or BC by 20, then, the hight AC remaining the 
same, the angles made by the transverse lines would be 
very slightly lessened. 



An apology is due the publishers for handing them a 
manuscript containing errors, which escaped correction. 
366.54750, page 8, should read 366.6351. On page 10 
43.693 should read 43.624, giving a difference of .181, 
instead of .215. In relation to the King's chamber, too, 
the cube I K L M should not only be divided by 2, but this 
again by 2, or, the original should suffer a division by 4 to 
make the chamber. The original cube would contain 8 
cubes, each equal to that of the ist difference: the King's 
chamber contains 2. The addition of the 80 must be 
made on the width or hight instead of on the length. 



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